Scheduling method in multiple access system and apparatus using the same

ABSTRACT

A method for allocating resources in a wireless communication system is provided. A base station receives a maximum transmission power from a first wireless device. The base station allocates a resource to the first wireless device based on a ratio of the maximum transmission power to a maximum available resource.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of priority of U.S. Provisionalapplication 61/550,379 filed on Oct. 22, 2011, all of which areincorporated by reference in their entirety herein.

BACKGROUND OF THE INVENTION

1. Field of the invention

The present invention relates to wireless communications, and moreparticularly, to a method and apparatus for optimum scheduling in awireless multiple access system.

2. Related Art

Wireless communication systems are widely spread all over the world toprovide various types of communication services such as voice or data.In general, the wireless communication system is a multiple accesssystem capable of supporting communication with multiple users bysharing available system resources (e.g., bandwidth, transmission power,etc.). Examples of the multiple access system include a code divisionmultiple access (CDMA) system, a frequency division multiple access(FDMA) system, a time division multiple access (TDMA) system, anorthogonal frequency division multiple access (OFDMA) system, a singlecarrier frequency division multiple access (SC-FDMA) system, etc.

Time-division multiple-access (TDMA) and code division multiple-access(CDMA) have been intensively studied for more than last three decades,and have been serving as the major multiple-access schemes for thesecond and the third generation wireless cellular systems, respectively.Recently, the fourth generation wireless cellular system has started tobe deployed worldwide, for which the frequency-division multiple-access(FDMA) serves in the form of discrete Fourier transform-spreadorthogonal frequency-division multiplexing, a.k.a., single-carrier FDMA.

Since the primary performance limiting factor of a CDMA system ismultiple-access interference (MAI), a lot of research has been conductedto mitigate the detrimental effect of the MAI through system parameteroptimizations. At the transmitter side, signature sequences have longbeen identified as important design parameters and hence optimized undervarious criteria.

SUMMARY OF THE INVENTION

The present invention provides a method and apparatus for optimumscheduling in a wireless multiple access system.

The present invention also provides a method and apparatus for acquiringmaximum sum rates of a constrained frequency-division multiple-access(FDMA), a constrained time division multiple-access (TDMA) and amulti-code code division multiple-access (CDMA).

In an aspect, a method for allocating resources in a wirelesscommunication system, is provided. The method comprises: receiving, by abase station from a first wireless device, a maximum transmission power;and allocating, by the base station, a resource to the first wirelessdevice based on a ratio of the maximum transmission power to a maximumavailable resource.

In another aspect, a base station for allocating resources in a wirelesscommunication system is provided. The base station comprises: a radiofrequency unit for receiving a radio signal; and a processor,operatively coupled with the radio frequency unit. The processor isconfigured to: receive from a first wireless device, a maximumtransmission power; and allocate a resource to the first wireless devicebased on a ratio of the maximum transmission power to a maximumavailable resource.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a wireless communication system.

FIG. 2 is a flow diagram illustrating the the method for allocatingresource by a base station in wireless communication system according toone embodiment of the present invention.

FIG. 3 is a flow diagram illustrating the method for allocating resourceby a base station in FDMA system according to one embodiment of thepresent invention.

FIG. 4 is a flow diagram illustrating the method for allocating resourcein CDMA system by the base station according to one embodiment of thepreset invention.

FIG. 5 is a block diagram showing the wireless communication system inwhich the embodiment of the present invention is implemented.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

The technology described below can be used for various multiple accessschemes including Code Division Multiple Access (CDMA), FrequencyDivision Multiple Access (FDMA), Time Division Multiple Access (TDMA),Orthogonal Frequency Division Multiple Access (OFMDA) and SingleCarrier-Frequency Division Multiple Access (SC-FDMA). CDMA can beimplemented by using such radio technology as UTRA (UniversalTerrestrial Radio Access) or CDMA2000. TDMA can be implemented by usingsuch radio technology as GSM (Global System for Mobilecommunications)/GPRS (General Packet Radio Service)/EDGE (Enhanced DataRates for GSM Evolution). OFDMA can be realized by using such radiotechnology as the IEEE 802.11 (Wi-Fi), IEEE 802.16 (WiMAX), IEEE 802.20,and E-UTRA (Evolved UTRA). UTRA is part of specifications for UMTS(Universal Mobile Telecommunications System). The 3GPP LTE is part ofE-UMTS (Evolved UMTS) using E-UTRA, which uses OFDMA radio access forthe downlink and SC-FDMA on the uplink. The LTE-A (Advanced) is anevolved version of the LTE.

FIG. 1 shows a wireless communication system. A wireless communicationsystem 10 includes at least one base station (BS) 11. Respective BSs 11provide communication services to specific geographical regions(generally referred to as cells) 15 a, 15 b, and 15 c. The cell can bedivided into a plurality of regions (referred to as sectors).

A user equipment (UE) 12 may be fixed or mobile, and may be referred toas another terminology, such as a mobile station (MS), a mobile terminal(MT), a user terminal (UT), a subscriber station (SS), a wirelessdevice, a personal digital assistant (PDA), a wireless modem, a handhelddevice, etc.

The BS 11 is generally a fixed station that communicates with the UE 12and may be referred to as another terminology, such as an evolved node-B(eNB), a base transceiver system (BTS), an access point, etc.

Hereinafter, downlink implies communication from the BS to the UE, anduplink implies communication from the UE to the BS. In the downlink, atransmitter may be a part of the BS, and a receiver may be a part of theUE. In the uplink, the transmitter may be a part of the UE, and thereceiver may be a part of the BS.

Meanwhile, in the general K-user FDMA system, total bandwidth of thesystem w_(tot) is given, and is divided to be assigned to K-users. Inthis FDMA system, the optimum method for assigning bandwidth is toallocate bandwidth in proportion to the power of each user. For example,if there are three users and the power of each user is p1=1, p2=2 and p3=3 respectively in FDMA system with total bandwidth w_(tot)=12, theoptimum method for allocating bandwidth will be to allocate bandwidth toeach user so that w1=2, w2=4 and w3=6 respectively.

In constrained FDMA system, however, there is one more constraint thangeneral FDMA system. In other words, constrained FDMA system imposeseach user upper limit in available bandwidth. For example, the kth usercannot have bandwidth exceeding w _(k). In this constrained FDMA system,the optimum method for allocating bandwidth for general FDMA system asdescribed above cannot be used.

Suppose that there is a Kuser FDMA system with total available systembandwidth w_(tot)>0[Hz] in real passband, the power of the kth userp_(k)>0, and the individual bandwidth constraint w _(k), for k=1, 2, . .. , K. Then, the maximum sum rate of constrained FDMA system can befound by solving

$\begin{matrix}{{Problem}\mspace{14mu} 1\text{:}} & \; \\{\underset{{(w_{k})}_{k}}{maximize}\; {\sum\limits_{k = 1}^{K}{w_{k}{\log \left( {1 + \frac{p_{k}}{\sigma^{2}w_{k}}} \right)}}}} & \left( {1a} \right) \\{{{{subject}\mspace{14mu} {to}\mspace{14mu} 0} \leq w_{k} \leq {\overset{\_}{w}}_{k}},{\forall k},{and}} & \left( {1b} \right) \\{{{\sum\limits_{k = 1}^{K}w_{k}} \leq w_{tot}},} & \left( {1c} \right)\end{matrix}$

where the decision parameter (w_(k))_(k) consists of the bandwidth w_(k)to be assigned to the kth user, for k=1, 2, . . . , K, and σ²>0 is thepower spectral density (PSD) of the additive white Gaussian noise (AWGN)that corrupts the complex baseband channel. The objective function isthe sum of the AWGN channel capacities of the users, so that the unit ofthe sum rate is [bits/second]. In (1a), we follow the convention

${{0 \cdot {\log \left( {1 + \frac{a}{0}} \right)}} = 0},{{{for}\mspace{14mu} {all}\mspace{14mu} a} \geq 0.}$

Without the individual bandwidth constraint, i.e., with (1b) beingreplaced by ∩≦w_(k), ∀k , the solution to Problem 1 is well known andgiven by

$\begin{matrix}{{w_{k,{opt}} = {\frac{p_{k}}{\sum\limits_{k^{\prime} = 1}^{K}}w_{tot}}},{\forall k},} & (2)\end{matrix}$

which is the proportional-share bandwidth allocation scheme, where eachuser is assigned bandwidth that is proportional to its signal power andthe system uses up all available system bandwidth.

There are two cases to consider with the individual bandwidth constraint(1b). For Σ_(k=1) ^(K) w _(k)≦w_(tot), it is obvious that the maximumsum rate is achieved by w_(k,opt)=w_(k), ∀k. Thus, it will be assumedthat

$\begin{matrix}{{\sum\limits_{k = 1}^{K}{\overset{\_}{w}}_{k}} > w_{tot}} & (3)\end{matrix}$

in what follows.

Lemma 1: The optimal solution (w_(k,opt))_(k) to Problem 1 always existsand is unique.

Proof Let f(x) be defined as

$\begin{matrix}{{f(x)}\overset{\Delta}{=}{x\; {\log \left( {1 + \frac{a}{x}} \right)}}} & (4)\end{matrix}$

where a >0 is a constant. Since log x≧1−1/x with equality if and only ifx=1 for x>0, direct differentiations lead to

$\begin{matrix}{{f^{\prime}(x)} = {{{\log \left( {1 + \frac{a}{x}} \right)} - \frac{a}{x + a}} > 0}} & \left( {5a} \right) \\{{{f^{''}(x)} = {{\frac{a}{\left( {x + a} \right)^{2}} - \frac{a}{x^{2} + {ax}}} < 0}},} & \left( {5b} \right)\end{matrix}$

for all x>0. Thus, the objective function in (1a) is concave because itsHessian matrix is diagonal with strictly negative diagonal entries.Moreover, the constraint set is convex. Therefore, the conclusionfollows from the theory of convex optimization.

As it is well known, the Karush-Kuhn-Tucker (KKT) conditions becomenecessary and sufficient for a feasible solution to be optimal in such aconcave maximization problem over a convex set if Slater's condition issatisfied.

Hereinafter, we provide the optimal solution in a closed algorithmicexpression and verify that it satisfies the KKT conditions.

It is assumed that the users are re-numbered in the decreasing order oftheir minimal PSDs (p_(k)/ w _(k))_(k), i.e.,

$\begin{matrix}{\frac{p_{1}}{{\overset{\_}{w}}_{1}} \geq \frac{p_{2}}{{\overset{\_}{w}}_{2}} \geq \ldots \geq {\frac{p_{K}}{{\overset{\_}{w}}_{K}}.}} & (6)\end{matrix}$

With this ordering, the kth user is tested by the rule

$\begin{matrix}{{{\hat{w}}_{k}\overset{\Delta}{=}{{\frac{p_{k}}{\sum\limits_{k^{\prime} = k}^{K}p_{k^{\prime}}}\left( {w_{tot} - {\sum\limits_{k^{\prime} = 1}^{k - 1}{\overset{\_}{w}}_{k^{\prime}}}} \right)}\underset{<}{\overset{>}{=}}{\overset{\_}{w}}_{k}}},} & (7)\end{matrix}$

and called

an oversized user, if

ŵ_(k)> w _(k),

a critically-sized user, if

ŵ_(k)= w _(k), and   (8)

an undersized user, if

ŵ_(k)< w _(k).

In (7) and in what follows, we adopt the convention that the sum Σ(·) iszero if the lower limit is greater than the upper limit.

Lemma 2: There exists κ∈{0, 1, . . . , K−1} such that

ŵ_(k)> w _(k), for 1≦k≦κ,  (9a)

ŵ_(k)≦ w _(k), for κ<k≦K.  (9b)

Proof First, we show that the test statistic ŵ_(k) satisfies

ŵ_(k)> w _(k)

ŵ_(l)> w _(l)∀l≦k, and  (10a)

ŵ_(k)≦ w _(k),

ŵ_(l)≦ w _(l)∀l≧k.  (10b)

Assume ŵ_(k)> w _(k). Then, for l∈{1, 2, . . . , k}, we have

$\begin{matrix}{{p_{k}\left( {w_{tot} - {\sum\limits_{k^{\prime} = 1}^{k - 1}{\overset{\_}{w}}_{k^{\prime}}}} \right)} > {{\overset{\_}{w}}_{k}{\sum\limits_{k^{\prime} = k}^{K}p_{k^{\prime}}}}} & \left( {11a} \right) \\\left. \Rightarrow{{p_{l}\left( {w_{tot} - {\sum\limits_{k^{\prime} = 1}^{k - 1}{\overset{\_}{w}}_{k^{\prime}}}} \right)} > {{\overset{\_}{w}}_{t}{\sum\limits_{k^{\prime} = k}^{K}p_{k^{\prime}}}}} \right. & \left( {11b} \right) \\\left. \Rightarrow{{{p_{l}\left( {w_{tot} - {\sum\limits_{k^{\prime} = 1}^{k - 1}{\overset{\_}{w}}_{k^{\prime}}}} \right)} + {p_{l}{\sum\limits_{k^{\prime} = 1}^{k - 1}{\overset{\_}{w}}_{k^{\prime}}}}} > {{{\overset{\_}{w}}_{l}{\sum\limits_{k^{\prime} = k}^{K}p_{k^{\prime}}}} + {{\overset{\_}{w}}_{l}{\sum\limits_{k^{\prime} = l}^{k - 1}p_{k^{\prime}}}}}} \right. & \left( {11c} \right) \\{\left. \Rightarrow{{p_{l}\left( {w_{tot} - {\sum\limits_{k^{\prime} = 1}^{l - 1}{\overset{\_}{w}}_{k^{\prime}}}} \right)} > {{\overset{\_}{w}}_{l}{\sum\limits_{k^{\prime} = l}^{K}p_{k^{\prime}}}}} \right.,} & \left( {11d} \right)\end{matrix}$

where (11b) and (11c) come from (6) and the assumption. Thus, ŵ_(l)> w_(l)holds.

Now, assume ŵ_(k)≦ w _(k). Then, for l∈{k+1, k+2, . . . , K}, we have

$\begin{matrix}{\mspace{79mu} {{p_{k}\left( {w_{tot} - {\sum\limits_{k^{\prime} = 1}^{k - 1}\; {\overset{\_}{w}}_{k^{\prime}}}} \right)} \leq {{\overset{\_}{w}}_{k}{\sum\limits_{k^{\prime} = k}^{K}p_{k^{\prime}}}}}} & \left( {12a} \right) \\{\mspace{79mu} \left. \Rightarrow{{p_{l}\left( {w_{tot} - {\sum\limits_{k^{\prime} = 1}^{k - 1}\; {\overset{\_}{w}}_{k^{\prime}}}} \right)} \leq {{\overset{\_}{w}}_{l}{\sum\limits_{k^{\prime} = k}^{K}p_{k^{\prime}}}}} \right.} & \left( {12b} \right) \\\left. \Rightarrow{{{p_{l}\left( {w_{tot} - {\sum\limits_{k^{\prime} = 1}^{k - 1}\; {\overset{\_}{w}}_{k^{\prime}}}} \right)} - {p_{l}{\sum\limits_{k^{\prime} = k}^{l - 1}\; {\overset{\_}{w}}_{k^{\prime}}}}} \leq {{{\overset{\_}{w}}_{l}{\sum\limits_{k^{\prime} = k}^{K}p_{k^{\prime}}}} - {{\overset{\_}{w}}_{l}{\sum\limits_{k^{\prime} = k}^{l - 1}p_{k^{\prime}}}}}} \right. & \left( {12c} \right) \\{\mspace{79mu} {\left. \Rightarrow{{p_{l}\left( {w_{tot} - {\sum\limits_{k^{\prime} = 1}^{l - 1}\; {\overset{\_}{w}}_{k^{\prime}}}} \right)} \leq {{\overset{\_}{w}}_{l}{\sum\limits_{k^{\prime} = l}^{K}p_{k^{\prime}}}}} \right.,}} & \left( {12d} \right)\end{matrix}$

where (12b) and (12c) come from (6) and the assumption. Thus, ŵ_(l)≦ w_(l) holds.

Second, we test the Kth user by the rule (7). Then, the channeloverloading assumption (3) leads to ŵ_(K)< w _(K). So, we evaluate ŵ_(k)from k=K−1 to k=1 to find the largest κ satisfying ŵ_(κ)> w _(κ). Ifsuch κ exists, then (9a) and (9b) hold. If not, then setting κ=0satisfies (9a) and (9b).

This lemma shows that there is a boundary index κ by which the oversizedand the non-oversized users are separated. In particular, every userwith index k≦κ is oversized, while every other user with index k>κ isnon-oversized.

In what follows, for notational simplicity, we denote the power and thebandwidth constraint profiles of users as

p

[p₁, p₂, . . . , p_(K)]^(T) and w

[ w ₁, w ₂, . . . , w _(K)]^(T),  (13)

respectively.

Theorem 1: Given P, w_(tot), and w, the optimal solution (w_(k,opt))_(k)and the maximized sum rate C_(FDMA)(p, w_(tot), w)are given by

$\begin{matrix}{\mspace{20mu} {w_{k,{opt}} = \left\{ {\begin{matrix}{{\overset{\_}{w}}_{k},} & {\forall{k \leq \kappa}} \\{{\frac{p_{k}}{\sum\limits_{k^{\prime} = {\kappa + 1}}^{K}p_{k^{\prime}}}\left( {w_{tot} - {\sum\limits_{k^{\prime} = 1}^{\kappa}{\overset{\_}{w}}_{k^{\prime}}}} \right)},} & {{\forall{k > \kappa}},}\end{matrix}\mspace{20mu} {and}} \right.}} & (14) \\{{{C_{FDMA}\left( {p,w_{tot},\overset{\_}{w}} \right)} = {{\sum\limits_{k = 1}^{\kappa}{{\overset{\_}{w}}_{k}{\log \left( {1 + \frac{p_{k}}{\sigma^{2}w_{k}}} \right)}}} + {\left( {w_{tot} - {\sum\limits_{k = 1}^{\kappa}{\overset{\_}{w}}_{k}}} \right){\log\left( {1 + \frac{\sum\limits_{k = {\kappa + 1}}^{K}p_{k}}{\sigma^{2}\left( {w_{tot} - {\sum\limits_{k = 1}^{\kappa}{\overset{\_}{w}}_{k}}} \right)}} \right)}}}},} & (15)\end{matrix}$

respectively, κ where is defined in Lemma 2.

Proof The constraints of Problem 1 satisfy Slater's condition. Thus, theKKT conditions of Problem 1 is necessary and sufficient for optimality.To proceed, we define the Lagrangian function

$\begin{matrix}{{{\mathcal{L}\left( {w_{k},\mu_{k},{\overset{\sim}{\mu}}_{k},\mu} \right)}\overset{\Delta}{=}{{\sum\limits_{k = 1}^{K}{w_{k}{\log \left( {1 + \frac{p_{k}}{\sigma^{2}w_{k}}} \right)}}} - {\sum\limits_{k = 1}^{K}{\mu_{k}\left( {w_{k} - {\overset{\_}{w}}_{k}} \right)}} + {\sum\limits_{k = 1}^{K}{{\overset{\sim}{\mu}}_{k}w_{k}}} - {\mu \left( {{\sum\limits_{k = 1}^{K}w_{k}} - w_{tot}} \right)}}},} & (16)\end{matrix}$

where (μ_(k))_(k), ({tilde over (μ)}_(k))_(k), and μ are the dualvariables. The KKT conditions for

Problem 1 are given by

$\begin{matrix}{{{{\log \left( {1 + \frac{p_{k}}{\sigma^{2}w_{k,{opt}}}} \right)} - \frac{p_{k}/w_{k,{opt}}}{\sigma^{2} + {p_{k}/w_{k,{opt}}}} - \mu_{k} + {\overset{\sim}{\mu}}_{k} - \mu} = 0},{\forall k},} & \left( {17a} \right) \\{{{w_{k,{opt}} - {\overset{\_}{w}}_{k}} \leq 0},{\forall k},} & \left( {17b} \right) \\{{w_{k,{opt}} \geq 0},{\forall k},} & \left( {17c} \right) \\{{{{\sum\limits_{k = 1}^{K}w_{k,{opt}}} - w_{tot}} \leq 0},} & \left( {17d} \right) \\{{\mu_{k} \geq 0},{\forall k},} & \left( {17e} \right) \\{{{\mu_{k}\left( {w_{k,{opt}} - {\overset{\_}{w}}_{k}} \right)} = 0},{\forall k},} & \left( {17f} \right) \\{{{\overset{\sim}{\mu}}_{k} \geq 0},{\forall k},} & \left( {17g} \right) \\{{{{\overset{\sim}{\mu}}_{k}w_{k,{opt}}} = 0},{\forall k},} & \left( {17h} \right) \\{{\mu \geq 0},{and}} & \left( {17i} \right) \\{{{\mu \left( {{\sum\limits_{k = 1}^{K}w_{k,{opt}}} - w_{tot}} \right)} = 0},} & \left( {17j} \right)\end{matrix}$

where (17a) is the stationarity condition, (17b), (17c), and (17d) arethe primal feasibility conditions, (17e), (17f), and (17g) are the dualfeasibility conditions, and (17h), (17i), and (17j) are thecomplementary slackness conditions.

Let d>0 be defined as

$\begin{matrix}{d\overset{\Delta \;}{=}{\frac{\sum\limits_{k = {\kappa + 1}}^{K}p_{k}}{w_{tot} - {\sum\limits_{k = 1}^{\kappa}{\overset{\_}{w}}_{k}}}.}} & (18)\end{matrix}$

The positivity of d will be shown below. Then, the optimal solution (14)can be rewritten as w_(k,opt)= w _(k), ∀k≦κ and w_(k,opt)=p_(k)/d,∀k>κ.Thus, d can be interpreted as the common PSD of non-oversized users.Now, we claim that (μ_(k))_(k), ({tilde over (μ)}_(k))_(k), and μ givenby

$\begin{matrix}{\mu_{k} = \left\{ \begin{matrix}\begin{matrix}{{\log \left( {1 + \frac{p_{k}}{\sigma^{2}w_{k}}} \right)} - \frac{p_{k}/{\overset{\_}{w}}_{k}}{\sigma^{2} + {p_{k}/{\overset{\_}{w}}_{k}}} -} \\{\left( {{\log \left( {1 + \frac{d}{\sigma^{2}}} \right)} - \frac{d}{\sigma^{2} + d}} \right),}\end{matrix} & {{\forall{k \leq \kappa}},} \\{0,} & {{\forall{k > \kappa}},}\end{matrix} \right.} & \left( {19a} \right) \\{{{\overset{\sim}{\mu}}_{k} = 0},{\forall k},{and}} & \left( {19b} \right) \\{{\mu = {{\log \left( {1 + \frac{d}{\sigma^{2\;}}} \right)} - \frac{d}{\sigma^{2} + d}}},} & \left( {19c} \right)\end{matrix}$

together with (14) satisfy all the KKT conditions in (17).

By evaluating the objective function with this solution, we obtain themaximized sum rate as (15).

Meanwhile, we extend the results to multi-code CDMA systems. Inmulti-code CDMA system, unlike single-code CDMA system, one user can useone or more of code. The number of codes that the kth user can use willbe represented by n _(k) below.

First, we establish a link with an FDMA system.

Suppose that there are K users in the system. It is assumed that the kthuser, for k=1, 2, . . . , K, can transmit upto n _(k) multiple datastreams by using multiple signature sequences. Thus, the received signalY is an N-by-1 random vector modeled by

$\begin{matrix}{{Y = {{\sum\limits_{k = 1}^{K}X_{k}} + N}},{and}} & \left( {22a} \right) \\{X_{k}\overset{\Delta}{=}{\sum\limits_{l = 1}^{{\overset{\_}{n}}_{k}}{d_{k,l}s_{k,l}}}} & \left( {22b} \right)\end{matrix}$

with d_(k,l) and S_(k,l) being the data symbol and the associatedsignature sequence of the lth stream of the kth user, respectively, andN being the additive circular-symmetric complex-Gaussian noise with meanzero and variance σ².

Define d_(k)

[d_(k,1), d_(k,2), . . . , d_(k, n) _(k) ]^(T) as the data symbolvector,

P_(k)

{d_(k)

}  (23a)

as the data symbol correlation matrix, and

S_(k)

[S_(k,1), S_(k,2), . . . , S_(k, n) _(k) ]  (23b)

as the signature sequence matrix of the kth user. Also define an(Σ_(k=1) ^(K) n _(k))-by-(Σ_(k=1) ^(K) n _(k)) matrix P and anN-by-(Σ_(k=1) ^(K) n _(k)) matrix S as

P

diag (P₁, P₂, . . . , P_(K)),  (24a)

S

[S₁, S₂, . . . , S_(K)]  (24b)

respectively. Note that P_(k) is not necessarily a diagonal matrixbecause the data symbol vector d_(k) of each user may consist ofcorrelated data symbols. It is assumed that the data symbol vectors(d_(k))_(k) are independent, which implies E{d_(k)

}=0, for k≠l, Since the signal correlation matrix of the kth user isgiven by E{X_(k)

}=S_(k)P_(k)

, the signal correlation matrix is given by

$\begin{matrix}{{SPS}^{H} = {\sum\limits_{k = 1}^{K}{S_{k}P_{k}{S_{k}^{H}.}}}} & (25)\end{matrix}$

Thus, the sum rate maximization problem for this synchronous multicodeCDMA system is formulated as

$\begin{matrix}{{Problem}\mspace{14mu} 2\text{:}} & \; \\{\underset{P,S}{{maximize}\;}\log \; {\det \left( {I + {\frac{1}{\sigma^{2}}{SPS}^{H}}} \right)}} & \left( {26a} \right) \\{{{{subject}\mspace{14mu} {to}\mspace{14mu} {{tr}\left( {S_{k}P_{k}S_{k}^{H}} \right)}} = p_{k}},{\forall k},} & \left( {26b} \right)\end{matrix}$

where p_(k) (>0), for k=1, 2, . . . , K, is the power of the kth user.

Lemma 3: Without loss of generality, we can restrict the search inProblem 2 for P and S to a diagonal matrix with non-negative entries andto a matrix with normalized column vectors, respectively.

By Lemma 3, P_(k) in (23a) can be written as

P_(k)=diag(p_(k,1), p_(k,2), . . . , p_(k, n) _(k) ),  (27)

where P_(k,1)

{|d_(k,l)|²} is the power of the lth data symbol of the kth user and,accordingly, we call P_(k) the power matrix of the kth user. So, we canreformulate Problem 2 as

$\begin{matrix}{{Problem}\mspace{14mu} 3\text{:}} & \; \\{\underset{P,S}{maximize}\; \log \; {\det \left( {I + {\frac{1}{\sigma^{2}}{SPS}^{H}}} \right)}} & \left( {28a} \right) \\{{{{subject}\mspace{14mu} {to}\mspace{14mu} {s_{k,l}}} = 1},{\forall k},{\forall l},} & \left( {28b} \right) \\{{{\sum\limits_{l = 1}^{{\overset{\_}{n}}_{k}}p_{k,l}} = p_{k}},{\forall k},{and}} & \left( {28c} \right) \\{{p_{k,l} \geq 0},{\forall k},{\forall l},} & \left( {28d} \right)\end{matrix}$

where the power matrix P is diagonal with non-negative entries, and thesignature sequence matrix S consists of normalized signature sequences.Proposition 1: For Σ_(k=1) ^(K) n _(k)≦N, the maximized sum rate isgiven by

$\begin{matrix}{{\sum\limits_{k = 1}^{K}{{\overset{\_}{n}}_{k}{\log \left( {1 + \frac{p_{k}}{\sigma^{2}{\overset{\_}{n}}_{k}}} \right)}}},} & (29)\end{matrix}$

which is achievable by jointly allocating the equal power among themulticodes of each user, i.e.,

$\begin{matrix}{{P_{k,{opt}} = {\frac{p_{k}}{{\overset{\_}{n}}_{k}}I_{{\overset{\_}{n}}_{k}}}},{\forall k},} & (30)\end{matrix}$

and by assigning Σ_(k=1) ^(K) n _(k) orthonormal signature sequences to{S_(k,l)}_(k,l), i.e.,

S_(opt)=I_(Σ) _(k=1) _(K) _(n) _(k) .  (31)

Proof: Since Σ_(k=1) ^(K) n _(k)≦N, each data symbol can be transmittedwithout suffering from any interference by assigning orthonormal codesto S_(k,l)∀k, ∀l. Then, the water-filling argument leads to theequal-power distribution among n _(k) multicodes of the kth user.

When Σ_(k=1) ^(K) n _(k)>N, the following proposition shows that themaximum sum rate as the optimal value of the seemingly complicatedmulticode CDMA problem Problem 3 can be obtained from the solution tothe FDMA problem Problem 1 by simply replacing w _(k) and w_(tot) with n_(k) and N, respectively.

Proposition 2: For Σ_(k=1) ^(K) n _(k)>N, the discrete-time synchronousmulticode CDMA system has the same maximum sum rate as the constrainedFDMA system given by

$\begin{matrix}{{Problem}\mspace{14mu} 4\text{:}} & \; \\{\max\limits_{{(w_{k})}_{k}}{\sum\limits_{k = 1}^{K}{w_{k}{\log \left( {1 + \frac{p_{k}}{\sigma^{2}w_{k}}} \right)}}}} & \left( {32a} \right) \\{{{{subject}\mspace{14mu} {to}\mspace{14mu} 0} \leq w_{k} \leq {\overset{\_}{n}}_{k}},{\forall k},} & \left( {32b} \right) \\{{\sum\limits_{k = 1}^{K}w_{k}} = {N.}} & \left( {32c} \right)\end{matrix}$

Proof: By converting Problem 3 into a double maximization problem, wehave

$\begin{matrix}{{Problem}\mspace{14mu} 5\text{:}} & \; \\{\underset{{(p_{k,l})}_{k,l}}{maximize}\left\{ \begin{matrix}\max\limits_{{(s_{k,l})}_{k,l}} & {\log \; {\det \left( {I + {\frac{1}{\sigma^{2}}{SPS}^{H}}} \right)}} \\{{subject}\mspace{14mu} {to}} & {{{s_{k,l}} = 1},{\forall k},{\forall l}}\end{matrix} \right.} & \left( {33a} \right) \\{{{{subject}\mspace{14mu} {to}\mspace{14mu} {\sum\limits_{l = 1}^{{\overset{\_}{n}}_{k}}p_{k,l}}} = p_{k}},{\forall k},{and}} & \left( {33b} \right) \\{{p_{k,l} \geq 0},{\forall k},{\forall{l.}}} & \left( {33c} \right)\end{matrix}$

Since (P_(k,l))_(k,l) is given and satisfies the conditions (33b) and(33c), the inner maximization problem of Problem 5 can be viewed as thesum-rate maximization problem for a critically- or over-loadedsingle-code CDMA system, which is already shown above to have the samemaximum sum rate as the FDMA system. So, if we follow the convention0·log(1+a/0)=0, for all a≧0, to make the single-user Gaussian channelcapacity a continuous function of the bandwidth, Problem 5 can berewritten as

$\begin{matrix}{{Problem}\mspace{14mu} 6\text{:}} & \; \\{\underset{{(p_{k,l})}_{k,l}}{maximize}\left\{ \begin{matrix}{\max\limits_{{(w_{k,l})}_{k,l}}{\sum\limits_{k = 1}^{K}{\sum\limits_{l = 1}^{{\overset{\_}{n}}_{k}}{w_{k,l}{\log \left( {1 + \frac{p_{k,l}}{\sigma^{2}w_{k,l}}} \right)}}}}} \\{{{{subject}\mspace{14mu} {to}\mspace{14mu} 0} \leq w_{k,l} \leq 1},{\forall k},{\forall l},{and}} \\{{\sum\limits_{k = 1}^{K}{\sum\limits_{l = 1}^{{\overset{\_}{n}}_{k}}w_{k,l}}} = N}\end{matrix} \right.} & \left( {34a} \right) \\{{{{subject}\mspace{14mu} {to}\mspace{14mu} {\sum\limits_{l = 1}^{{\overset{\_}{n}}_{k}}p_{k,l}}} = p_{k}},{\forall k},} & \left( {34b} \right) \\{{p_{k,l} \geq 0},{\forall k},{\forall{l.}}} & \left( {34c} \right)\end{matrix}$

If we rewrite Problem 6 as a single maximization problem and find thealternative double maximization problem, it can be written as

$\begin{matrix}{{Problem}\mspace{14mu} 7\text{:}} & \; \\{\underset{{(w_{k,l})}_{k,l}}{maximize}\left\{ \begin{matrix}\begin{matrix}{\max\limits_{{(p_{k,l})}_{k,l}}{\sum\limits_{k = 1}^{K}{\sum\limits_{l = 1}^{{\overset{\_}{n}}_{k}}{w_{k,l}{\log \left( {1 + \frac{p_{k,l}}{\sigma^{2}w_{k,l}}} \right)}}}}} \\{{{{subject}\mspace{14mu} {to}\mspace{14mu} {\sum\limits_{l = 1}^{{\overset{\_}{n}}_{k}}p_{k,l}}} = p_{k}},{\forall k},{and}}\end{matrix} \\{{p_{k,l} \geq 0},{\forall k},{\forall l},}\end{matrix} \right.} & \left( {35a} \right) \\{{{{subject}\mspace{14mu} {to}\mspace{14mu} 0} \leq w_{k,l} \leq 1},{\forall k},{\forall l},{and}} & \left( {35b} \right) \\{{\sum\limits_{k = 1}^{K}{\sum\limits_{l = 1}^{{\overset{\_}{n}}_{k}}w_{k,l}}} = N} & \left( {35c} \right)\end{matrix}$

The closed-form solution to the inner maximization of Problem 7 can beeasily found as

$\begin{matrix}{{p_{k,l,{opt}} = {\frac{w_{k,l}}{\sum\limits_{l^{\prime} = 1}^{{\overset{\_}{n}}_{k}}w_{k,l^{\prime}}}p_{k}}},{\forall k},{\forall l},} & (36)\end{matrix}$

by applying the Karush-Kuhn-Tucker conditions. This solution can beinterpreted, for each k, as a water-filling solution to parallelGaussian channels with bandwidths (w_(k,l))_(l=1) ^(n) ^(k) and commonnoise density σ².

By plugging in (36) to Problem 7, we have

$\begin{matrix}{{Problem}\mspace{14mu} 8\text{:}} & \; \\{\underset{{(w_{k,l})}_{k,l}}{maximize}{\sum\limits_{k = 1}^{K}{\sum\limits_{l = 1}^{{\overset{\_}{n}}_{k}}{w_{k,l}{\log\left( {1 + \frac{p_{k}}{\sigma^{2}{\sum\limits_{l^{\prime} = 1}^{{\overset{\_}{n}}_{k}}w_{k,l^{\prime}}}}} \right)}}}}} & \left( {37a} \right) \\{{{{subject}\mspace{14mu} {to}\mspace{14mu} 0} \leq w_{k,l} \leq 1},{\forall k},{\forall l},{and}} & \left( {37b} \right) \\{{\sum\limits_{k = 1}^{K}{\sum\limits_{l = 1}^{{\overset{\_}{n}}_{k}}w_{k,l}}} = {N.}} & \left( {37c} \right)\end{matrix}$

Define w_(k) as

$\begin{matrix}{{w_{k}\overset{\Delta}{=}{\sum\limits_{l = 1}^{{\overset{\_}{n}}_{k}}w_{k,l}}},} & (38)\end{matrix}$

for k=1, 2, . .. , K. Then, it can be immediately seen that theobjective function in (37a) is a function only of (w_(k))_(k=1) ^(K).Moreover, the constraint (37b) implies

0≦w_(k)≦ n _(k), ∀k,  (39)

which can be imposed on Problem 8 as an additional constraint withoutaltering the maximum sum rate. Thus, the maximum sum rate can be foundby solving Problem 4 as far as the optimal solution (w_(k,opt))_(k=1)^(K) guarantees the existence of (w_(k,l,opt))_(k,l) such that

$\begin{matrix}{{w_{k,{opt}} = {{\sum\limits_{l = 1}^{{\overset{\_}{n}}_{k}}{w_{k,l,{opt}}\mspace{14mu} {and}\mspace{14mu} 0}} \leq w_{k,l,{opt}} \leq 1}},} & (40)\end{matrix}$

∀k, ∀l. It can be easily verified that

${w_{k,l,{opt}} = \frac{w_{{k,{opt}}\;}}{{\overset{\_}{n}}_{k}}},{\forall k},{\forall l},$

always satisfies the constraint (40).

The following corollary provides the maximized sum rate of the K-usermulticode CDMA system in terms of the power profile (p_(k))_(k=1) ^(K)and the maximum allowable multicodes ( n _(k))_(k=1) ^(K) per user.

Corollary 1: For Σ_(k=1) ^(K) n _(k)>N, the maximized sum rate is givenby

$\begin{matrix}{{\sum\limits_{k = 1}^{\kappa}{{\overset{\_}{n}}_{k}{\log \left( {1 + \frac{p_{k}}{\sigma^{2}{\overset{\_}{n}}_{k}}} \right)}}} + {\left( {N - {\sum\limits_{k = 1}^{\kappa}{\overset{\_}{n}}_{k}}} \right){\log\left( {1 + \frac{p_{tot} - {\sum\limits_{k = 1}^{\kappa}p_{k}}}{\sigma^{2}\left( {N - {\sum\limits_{k = 1}^{\kappa}{\overset{\_}{n}}_{k}}} \right)}} \right)}}} & (41)\end{matrix}$

where the users are re-numbered so that

$\begin{matrix}{\frac{p_{1}}{{\overset{\_}{n}}_{1}} \geq \frac{p_{2}}{{\overset{\_}{n}}_{2}} \geq \ldots \geq \frac{p_{K}}{{\overset{\_}{n}}_{K}}} & (42)\end{matrix}$

and κ is the largest user index satisfying the testing rule

$\begin{matrix}{{\frac{p_{\kappa \;}}{\sum\limits_{k = \kappa}^{K}p_{k}}\left( {N - {\sum\limits_{k = 1}^{\kappa - 1}{\overset{\_}{n}}_{k}}} \right)} \geq {{\overset{\_}{n}}_{\kappa}.}} & (43)\end{matrix}$

If there exists no such κ, then we set κ=0 in (42).

Proof It is straightforward to obtain (41) by combining Theorem 1 andProposition 2.

Note that, if we adopt the convention Σ_(k=K+1) ^(K)(·)=0, the maximumsum rate (41) for Σ_(k=1) ^(K) n _(k)>N is also applicable to the caseswith Σ_(k=1) ^(K) n _(k)≦N because (43) results in κ=K, which leads tothe maximum sum rate (29).

The associated optimal multicode system is characterized as follows.

Corollary 2: For Σ_(k=1) ^(K) n _(k)>N, the maximized sum rate isachievable by jointly allocating the power (P_(k))_(k=1) ^(K) among themulticodes of each user as

$\begin{matrix}{P_{k,{opt}} = {{diag}\left( {{\frac{w_{k,1,{opt}}}{w_{k,{opt}}}p_{k}},{\frac{w_{k,2,{opt}}}{w_{{k,{opt}}\;}}p_{k}},\ldots \mspace{14mu},{\frac{w_{k,{\overset{\_}{n}}_{k},{opt}}}{w_{k,{opt}}}p_{k}}} \right)}} & (44)\end{matrix}$

for k=1, 2, . . . , K, where w_(k,opt) is given by

$\begin{matrix}{w_{k,{opt}} = \left\{ \begin{matrix}{{\overset{\_}{n}}_{k},} & {\forall{k \leq \kappa}} \\{{\frac{p_{k}}{\sum\limits_{k^{\prime} = {\kappa + 1}}^{K}p_{k^{\prime}}}\left( {N - {\sum\limits_{k^{\prime} = 1}^{\kappa}{\overset{\_}{n}}_{k^{\prime}}}} \right)},} & {{\forall{k > \kappa}},}\end{matrix} \right.} & (45)\end{matrix}$

and w_(k,l,opt) can be chosen arbitrary that satisfy

$\begin{matrix}{{{\sum\limits_{l = 1}^{{\overset{\_}{n}}_{k}}w_{k,l,{opt}}} = {{w_{k,{opt}}\mspace{14mu} {and}\mspace{14mu} 0} \leq w_{k,l,{opt}} \leq 1}},} & (46)\end{matrix}$

∀k,∀l and by assigning (S_(k,l,opt))_(k,l) as

$\begin{matrix}{s_{k,l,{opt}} = \left\{ \begin{matrix}{{{arbitrary}\mspace{14mu} {orthonormal}\mspace{14mu} {vector}},} & {{{for}\mspace{14mu} \left( {k,l} \right)} \in K} \\{{\sum\limits_{m = 1}^{N - {K}}{{\overset{\sim}{s}}_{k,l,m}e_{m}}},} & {{{{for}\mspace{14mu} \left( {k,l} \right)} \notin K},}\end{matrix} \right.} & (47)\end{matrix}$

where κ is defined as

κ={(k,l):w _(k,l,opt)=1,1≦k≦K,1≦l≦ n _(k)}  (48)

and (e_(m))_(m=1) ^(N−|κ|) is any orthonormal basis of (N−|κ|)dimensional subspace that is orthogonal to the subspace spanned by(S_(k,l,opt))_((k,l)∈)κ, and {hacek over (S)}_(k,l,m) the mth entry ofthe sequence {tilde over (S)}_(k,l) of length N−|κ| such that

$\begin{matrix}{{\sum\limits_{{({k,l})} \notin K}{p_{k,l,{opt}}{\overset{\sim}{s}}_{k,l}{\overset{\sim}{s}}_{k,l}^{H}}} = {\frac{\sum_{{({k,l})} \notin K}p_{k,l,{opt}}}{N - {K}}{I_{N - {K}}.}}} & (49)\end{matrix}$

Here, from (46) the optimal number of multicodes corresponding to thekth user is given by

$\begin{matrix}{\sum\limits_{l = 1}^{{\overset{\_}{n}}_{k}}{{sgn}\left( w_{k,l,{opt}} \right)}} & (50)\end{matrix}$

Corollary 3: For multicode CDMA without restriction on number ofmulticodes per user, the maximized sum rate is achievable by jointlyallocating the power (p_(k))_(k=1) ^(K) among the multicodes of eachuser as

$\begin{matrix}{P_{k,{opt}} = {{diag}\left( {{\frac{w_{k,1,{opt}}}{w_{k,{opt}}}p_{k}},{\frac{w_{k,2,{opt}}}{w_{k,{opt}}}p_{k}},\ldots \mspace{14mu},{\frac{w_{k,n_{k,{opt}},{opt}}}{w_{k,{opt}}}p_{k}}} \right)}} & (51)\end{matrix}$

for k=1, 2, . . . , K, where n_(k,opt) can be chosen arbitrary thatsatisfy

$\begin{matrix}{n_{k} \geq \left\lceil {\frac{p_{k}}{\sum\limits_{k^{\prime} = 1}^{K}p_{k^{\prime}}}w_{tot}} \right\rceil} & (52)\end{matrix}$

and w_(k,opt) is given by

$\begin{matrix}{w_{k,{opt}} = \left\{ \begin{matrix}{n_{k,{opt}},} & {\forall{k \leq \kappa}} \\{{\frac{p_{k}}{\overset{K}{\sum\limits_{k^{\prime} = {\kappa + 1}}}p_{k^{\prime}}}\left( {N - {\sum\limits_{k^{\prime} = 1}^{\kappa}n_{k^{\prime},{opt}}}} \right)},} & {{\forall{k > \kappa}},}\end{matrix} \right.} & (53)\end{matrix}$

and w_(k,l,opt) can be chosen arbitrary that satisfy

$\begin{matrix}{{{\sum\limits_{l = 1}^{n_{k,{opt}}}\; w_{k,l,{opt}}} = w_{k,{opt}}}\mspace{14mu} {and}{{0 \leq w_{k,l,{opt}} \leq 1},}} & (54)\end{matrix}$

∀k, ∀l and by assigning (s_(k,l,opt))_(k,l) as

$\begin{matrix}{s_{k,l,{opt}} = \left\{ \begin{matrix}{{{arbitrary}\mspace{14mu} {orthonormal}\mspace{14mu} {vector}},} & {{{for}\mspace{14mu} \left( {k,l} \right)} \in \kappa} \\{{\sum\limits_{m = 1}^{N - {\kappa }}\; {{\overset{\sim}{s}}_{k,l,m}e_{m}}},} & {{{for}\mspace{14mu} \left( {k,l} \right)} \notin {\kappa.}}\end{matrix} \right.} & (55)\end{matrix}$

where κ is defined as

κ={(k,l):w_(k,l,opt)=1,1≦k≦K,1≦l≦n _(k,opt)}  (56)

and (e_(m))_(m=1) ^(N−|κ|) is any orthonormal basis of (N−|κ|)dimensional subspace that is orthogonal to the subspace spanned by(S_(k,l,opt))_((k,l)∈)κ, and {tilde over (S)}_(k,l,m) is the mth entryof the sequence {tilde over (S)}_(k,l) of length N−|κ| such that

$\begin{matrix}{{\sum\limits_{{({k,l})} \notin \kappa}\; {p_{k,l,{opt}}{\overset{\sim}{s}}_{k,l}{\overset{\sim}{s}}_{k,l}^{H}}} = {\frac{\sum\limits_{{({k,l})} \notin \kappa}\; p_{k,l,{opt}}}{N - {\kappa }}{I_{N - {\kappa }}.}}} & (57)\end{matrix}$

Various embodiments of the present invention will be described belowbased on the optimal solution on the problems described above.

FIG. 2 is a flow diagram illustrating the the method for allocatingresource by a base station in wireless communication system according toone embodiment of the present invention.

A base station receives information on maximum transmission power fromthe wireless device (S210).

The base station determines resource allocation priority of the wirelessdevice based on the ratio of the maximum transmission power to a maximumavailable resource (S220).

The base station allocates resource to the wireless device based on theresource allocation priority (S230). In other words, the base stationallocates resource to the wireless device based on the ratio of themaximum transmission power to a maximum available resource. At thisstep, the resource allocated to the wireless device may be determinedbased on the maximum transmission power of the wireless device, a sizeof resources not allocated yet, and a sum of maximum transmission powersof wireless devices having lower resource allocation priorities.

The method for allocating resource in constrained FDMA system will bedescribed in more detail. FIG. 3 is a flow diagram illustrating themethod for allocating resource by a base station in FDMA systemaccording to one embodiment of the present invention.

As described above, there are constraints of transmission power andavailable bandwidth for each wireless device in constrained FDMA system.In other words, maximum transmission power p_(k) and maximum availablebandwidth w_(k) are imposed on each device. In order to get maximumtransmission rate for the entire wireless devices, i.e., the totalsystem, in scheduling resource for multiple access, the base stationallocates bandwidth based on the ratio of the maximum transmission powerto a maximum available bandwidth.

The base station receives the information on maximum transmission powerfrom wireless device (S310).

The base station determines bandwidth allocation priority of thewireless device based on the ratio of the maximum transmission power toa maximum available bandwidth (S320). For example, the base station canarrange wireless devices based on the size of the minimum PSD of eachwireless device, and allocate bandwidth to the arranged wirelessdevices. At this step, bandwidth is allocated to the wireless devicessequentially from the

devices with large size of

$\frac{p_{k}}{\overset{\_}{w_{k}}}$

value to the devices with small size of the value.

The base station allocates bandwidth to the wireless device based on thebandwidth allocation priority S330.

For example, the base station can determine the bandwidth w_(k)allocated to the wireless device by the following equation, as explainedin (14).

$\begin{matrix}{w_{k} = {\frac{p_{k}}{\sum\limits_{k^{\prime} = {\kappa + 1}}^{K}\; p_{k^{\prime}}}\left( {w_{tot} - {\sum\limits_{k^{''} = 1}^{\kappa}\overset{\_}{w_{k^{''}}}}} \right)}} & \left\lbrack {{Equation}\mspace{14mu} 58} \right\rbrack\end{matrix}$

where p_(k) is the maximum transmission power of the wireless device, κis a number of wireless devices using maximum transmission powers,p_(k′) is a maximum transmission power of a wireless device having k′thresource allocation priority, w_(tot) is a total available systembandwidth, and w_(k″) a maximum available bandwidth of a wireless devicehaving k″th resource allocation priority.

In another example, the base station can determine the bandwidth w_(k)allocated to the wireless device by the following equation.

$\begin{matrix}{w_{k} = {w_{retotal}\left( \frac{p_{k}}{p_{retotal}} \right)}} & \left\lbrack {{Equation}\mspace{14mu} 59} \right\rbrack\end{matrix}$

where p_(k) is the maximum transmission power of the wireless device,W_(retotal) is the size of resources not allocated yet, and p_(retotal)is the sum of maximum transmission powers of the wireless devices whichare remained in the process of sequential bandwidth allocation, i.e.,the sum of maximum transmission powers of wireless devices having lowerresource allocation priorities.

At this step, the allocated bandwidth cannot exceed the maximumavailable bandwidth w_(k) . In other words, if the bandwidth determinedby the above equations is larger than w_(k) , the base station allocatesw_(k) to the kth wireless device.

Meanwhile, the method for allocating resource in multi-code CDMA systemis described below. FIG. 4 is a flow diagram illustrating the method forallocating resource in CDMA system by the base station according to oneembodiment of the preset invention. For the convenience of explanation,description will be made separately on the multi-code CDMA system inwhich the number of codes to be used by each wireless device is limitedand the multi-code CDMA system in which the number of codes to be usedby each wireless device is not limited.

First, explanation will be made on the method for scheduling resourcefor the multi-code CDMA system in which the transmission power of eachwireless device and the number of codes to be used by each wirelessdevice is limited and the length of each code is fixed. In the below,p_(k) means the maximum transmission power of the kth wireless device,n_(k) the maximum number of available codes of the kth wireless device,and N the length of each code.

The base station receives information on the maximum transmission powerfrom the wireless device (S410).

In order to acquire maximum transmission for the entire wirelessdevices, i.e., the total system, the base station determines allocationpriority of the wireless device based on the ratio of the maximumtransmission power to a maximum number of available codes (S420). Forexample, the base station can arrange the wireless devices in decreasingorder

of the value

$\frac{p_{k}}{\overset{\_}{n_{k}}}$

of the wireless devices.

The base station determines the number of codes to be used by eachwireless device and the power to be allocated to each code based on theallocation priority (S430, S440). In the next steps, the code to be usedby each wireless device is designed based on the number of codes and thepower, which have been determined (S450).

For example, the base station can determine, in step S430, the number ofcodes, n_(k), to be used by the kth wireless device by the followingequation, as explained in (45).

$\begin{matrix}{w_{k} = {\frac{p_{k}}{\sum\limits_{k^{\prime} = {\kappa + 1}}^{K}\; p_{k^{\prime}}}\left( {N - {\sum\limits_{k^{''} = 1}^{\kappa}n_{k^{''}}}} \right)}} & \left\lbrack {{Equation}\mspace{14mu} 60} \right\rbrack\end{matrix}$

where p_(k) is the maximum transmission power of the wireless device, κis a number of wireless devices using maximum transmission powers,p_(k′) is a maximum transmission power of a wireless device having k′thresource allocation priority, N is a length of each code, and n_(k″) isa maximum number of available codes of a wireless device having k″thresource allocation priority.

In yet another example, the base station can, in step S430, determinethe number of codes n_(k) to be used by the kth wireless device by thefollowing equation based on the value m_(k) represented by the equation.

$\begin{matrix}{m_{k} = {N_{retotal}\left( \frac{p_{k}}{p_{retotal}} \right)}} & \left\lbrack {{Equation}\mspace{14mu} 61} \right\rbrack\end{matrix}$

where N_(retotal) is the value remained by subtracting m_(k) ofpreceding devices from the process gain N in the process of sequentialallocation of the number of codes, i.e., the value subtracted a sum ofvalues m_(k)s of wireless devices having higher resource allocationpriorities from the length of each code N (N_(retotal)=N−m₁−m₁−m₂− . . .−m_(k-l)), p_(k) is the maximum transmission power of the wirelessdevice, p_(retotal) is the sum of transmission power of remainingwireless devices including the corresponding wireless device, i.e., thesum of the maximum transmission powers of the first wireless device andthe second wireless devices (p_(retotal)=p_(k)+p_(k+1)+ . . . +p_(k)).

Meanwhile, the number of codes, n_(k), to be used by the kth wirelessdevice cannot exceed maximum number of available codes n_(k) . So, ifthe value of m_(k) is greater than n_(k) , the number of codes, n_(k),to be used by the kth wireless device is determined as n_(k) . If thevalue of m_(k) is smaller than or equal to n_(k) , however, the numberof codes, n_(k), to be used by the kth wireless device is determined asan arbitrary natural number which is greater than or equal to the valueof m_(k) and smaller than or equal to the value of n_(k) .

In order to determine the power to be allocated to each code of the kthwireless device in step S440, the base station can determine the ratioby which maximum transmission power p_(k) is divided among n_(k) ofcodes. At this step, the ratio of each code cannot exceed the reciprocalof the value of m_(k) described in the step S430, and the ratios sums upto 1.

For example, in the case where n_(k) is 5 and m_(k) is 4, if the basestation determines the ratio allocated to the 5 codes as 0.2, 0.2, 0.2,0.2 and 0.2 respectively, the ratios are valid since the value of eachratio is smaller than 0.25 which is the reciprocal of the value ofm_(k). However, if the base station determines the ratio allocated tothe 5 codes as 0.3, 0.3, 0.2, 0.1 and 0.1 respectively, the ratios areinvalid since there exist ratios whose value are greater than 0.25 whichis the reciprocal of the value of m_(k).

Then, the base station determines the power to be allocated to each codebased on the ratio determined. Also, the base station designs, in thestep S450, the code to be used by the wireless device. At this step,orthogonal codes with length of N are allocated to the codes in whichthe ratio determined at the step S440 have value corresponding to thereciprocal of m_(k), and Quansi-orthogonal sequences satisfyinggeneralized Welch bound equality are allocated to the collection ofcodes having smaller value than the reciprocal of m_(k). The reason forthis kind of allocation is that maximum of N orthogonal vectors can bemade in N-dimensional vector space, and that every vector cannot beorthogonal each other when the number of vectors to be designed is morethan N. Therefore, the base station designs the code by usingQuasi-orthogonal sequence, as explained in (55) through (57).

Now, explanation will be made on the method for scheduling resource forthe multi-code CDMA system in which the transmission power of eachwireless device is limited and the length of each code is fixed, but thenumber of codes to be used by each wireless device is not limited.

The process of step S410, in which the base station receives informationon maximum transmission power from the wireless device, is the same asthe process in the multi-code CDMA system with the limit on the numberof codes.

In order to acquire maximum transmission for the entire wirelessdevices, i.e., the total system, the base station determines allocationpriority of the wireless device based on the maximum transmission power(S420). For example, the base station can arrange wireless devices indecreasing order of the size of maximum transmission power p_(k) of thewireless devices. Since there is no maximum number of available codesn_(k) in multi-code CDMA system with no limit on the code, the size ofmaximum transmission power p_(k) becomes the standard for allocationpriority.

In the same way, the base station determines the number of codes to beused by each wireless device and the power to be allocated to each codebased on the allocation priority (S430, S440). Then, the base stationdesigns the code to be used by each wireless device based on the numberof codes and power which have been determined in the previous steps(S450).

For example, the base station determines, at the step S430, the numberof codes n_(k) to be used by the kth wireless device based on the valuem_(k) represented by the following equation.

$\begin{matrix}{m_{k} = {N_{retotal}\left( \frac{p_{k}}{p_{retotal}} \right)}} & \left\lbrack {{Equation}\mspace{14mu} 62} \right\rbrack\end{matrix}$

where N_(retotal) is the value remained by subtracting m_(k) ofpreceding devices from the process gain N in the process of sequentialallocation of the number of codes, i.e., the value subtracted a sum ofvalues m_(k)s of wireless devices having higher resource allocationpriorities from the length of each code N (N_(retotal)=N−m₁−m₁−m₂− . . .−m_(k-l)), p_(k) is the maximum transmission power of the wirelessdevice, p_(retotal) is the sum of transmission power of remainingwireless devices including the corresponding wireless device, i.e., thesum of the maximum transmission powers of the first wireless device andthe second wireless devices (p_(retotal)=p_(k)=p_(k+1)+ . . . +p_(k)).

Finally, the number of codes n_(k) to be used by the kth wireless deviceis determined as an arbitrary natural number which is greater than orequal to the value m_(k).

FIG. 5 is a block diagram showing the wireless communication system inwhich the embodiment of the present invention is implemented.

The base station 50 includes a processor 51, memory 52 and RF (radiofrequency) unit 53. The memory 52 is connected to the processor 51, andstores various information for driving the processor 51. The RF unit 53is connected to the processor 51, and transmits and/or receives radiosignal. The processor 51 implements proposed functions, proceduresand/or methods. In the embodiments from FIG. 2 to FIG. 4, the operationof the wireless device can be implemented by the processor 51.

The wireless device 60 includes a processor 61, memory 62 and RF unit63. The memory 62 is connected to the processor 61, and stores variousinformation for driving the processor 61. The RF unit 63 is connected tothe processor 61, and transmits and/or receives radio signal. Theprocessor 61 implements proposed functions, procedures and/or methods.In the embodiments from FIG. 2 to FIG. 4, the operation of the wirelessdevice can be implemented by the processor 61.

The processor may include application-specific integrated circuit(ASIC), other chipset, logic circuit and/or data processing device. Thememory may include read-only memory (ROM), random access memory (RAM),flash memory, memory card, storage medium and/or other storage device.The RF unit may include baseband circuitry to process radio frequencysignals. When the embodiments are implemented in software, thetechniques described herein can be implemented with modules (e.g.,procedures, functions, and so on) that perform the functions describedherein. The modules can be stored in memory and executed by processor.The memory can be implemented within the processor or external to theprocessor in which case those can be communicatively coupled to theprocessor via various means as is known in the art.

In view of the exemplary systems described herein, methodologies thatmay be implemented in accordance with the disclosed subject matter havebeen described with reference to several flow diagrams. While forpurposed of simplicity, the methodologies are shown and described as aseries of steps or blocks, it is to be understood and appreciated thatthe claimed subject matter is not limited by the order of the steps orblocks, as some steps may occur in different orders or concurrently withother steps from what is depicted and described herein. Moreover, oneskilled in the art would understand that the steps illustrated in theflow diagram are not exclusive and other steps may be included or one ormore of the steps in the example flow diagram may be deleted withoutaffecting the scope and spirit of the present disclosure.

What is claimed is:
 1. A method for allocating resources in a wireless communication system, the method comprising: receiving, by a base station from a first wireless device, a maximum transmission power; and allocating, by the base station, a resource to the first wireless device based on a ratio of the maximum transmission power to a maximum available resource.
 2. The method of claim 1, further comprising: determining, by the base station, an resource allocation priority of the first wireless device based on the ratio.
 3. The method of claim 2, wherein the resource allocated to the first wireless device is determined based on the maximum transmission power of the first wireless device, a size of resources not allocated yet, and a sum of maximum transmission powers of second wireless devices having lower resource allocation priorities than the first wireless device.
 4. The method of claim 2, wherein the resource allocated to the first wireless device is based on a bandwidth in a Frequency Division Multiple Access (FDMA) system.
 5. The method of claim 4, wherein the resource allocated to the first wireless device w_(k) is determined by the following equation, the first wireless device having kth resource allocation priority in K-user FDMA system: $w_{k} = {\frac{p_{k}}{\sum\limits_{k^{\prime} = {\kappa + 1}}^{K}\; p_{k^{\prime}}}\left( {w_{tot} - {\sum\limits_{k^{''} = 1}^{\kappa}\overset{\_}{w_{k^{''}}}}} \right)}$ where p_(k) is the maximum transmission power of the first wireless device, κ is a number of wireless devices using maximum transmission powers, p_(k′) is a maximum transmission power of a wireless device having k′th resource allocation priority, w_(tot) is a total available system bandwidth, and w_(k″) is a maximum available bandwidth of a wireless device having k″th resource allocation priority.
 6. The method of claim 4, wherein the resource allocated to the first wireless device w_(k) is determined by the following equation, the first wireless device having kth resource allocation priority in K-user FDMA system: $w_{k} = {w_{retotal}\left( \frac{p_{k}}{p_{retotal}} \right)}$ where p_(k) is the maximum transmission power of the first wireless device, w_(retotal) is a size of resources not allocated yet, and p_(retotal) is a sum of maximum transmission powers of second wireless devices having lower resource allocation priorities than the first wireless device.
 7. The method of claim 2, wherein the resource allocated to the first wireless device is based on a number of codes in a Code Division Multiple Access (CDMA) system.
 8. The method of claim 7, wherein the resource allocated to the first wireless device w_(k) is determined by the following equation, the first wireless device having kth resource allocation priority in K-user CDMA system: $w_{k} = {\frac{p_{k}}{\sum\limits_{k^{\prime} = {\kappa + 1}}^{K}\; p_{k^{\prime}}}\left( {N - {\sum\limits_{k^{''} = 1}^{\kappa}n_{k^{''}}}} \right)}$ where p_(k) is the maximum transmission power of the first wireless device, κ is a number of wireless devices using maximum transmission powers, p_(k′) is a maximum transmission power of a wireless device having k′th resource allocation priority, N is a length of each code, and n_(k″) is a maximum number of available codes of a wireless device having k″th resource allocation priority.
 9. The method of claim 7, wherein the resource allocated to the first wireless device is determined based on a length of each code, a sum of maximum transmission powers of the first wireless device and second wireless devices having lower resource allocation priorities than the first wireless device.
 10. The method of claim 9, wherein the resource allocated to the first wireless device is determined as a natural number which is greater than or equal to a value m_(k) represented by the following equation, the first wireless device having kth resource allocation priority in K-user CDMA system: $m_{k} = {N_{retotal}\left( \frac{p_{k}}{p_{retotal}} \right)}$ where N_(retotal) is a value subtracted a sum of values m_(k)s of third wireless devices having higher resource allocation priorities than the first wireless device from the length of each code N, p_(k) is the maximum transmission power of the first wireless device, and p_(retotal) is the sum of the maximum transmission powers of the first wireless device and the second wireless devices.
 11. The method of claim 10, wherein a power ratio allocated to each code does not exceed a reciprocal of the value m_(k).
 12. The method of claim 1, wherein the resource allocated to the first wireless device does not exceed the maximum available resource.
 13. A base station for allocating resources in a wireless communication system, the base station comprising: a radio frequency unit for receiving a radio signal; and a processor, operatively coupled with the radio frequency unit, configured to: receive from a first wireless device, a maximum transmission power; and allocate a resource to the first wireless device based on a ratio of the maximum transmission power to a maximum available resource.
 14. The base station of claim 13, wherein the processor is configured to: determine an resource allocation priority of the first wireless device based on the ratio, wherein the resource allocated to the first wireless device is determined based on the maximum transmission power of the first wireless device, a size of resources not allocated yet, and a sum of maximum transmission powers of second wireless devices having lower resource allocation priorities than the first wireless device. 